A better parallel, particularly after the chase begins, is with the classic screwball comedy of the 1930s and 1940s: The Awful Truth, Bringing Up Baby, His Girl Friday.
Instead, there's a kinship with Hollywood's screwball comedies of the 1930s, where an unlikely romance blossoms in the flurries of a rough and tumble escapade, like the beautiful zaniness of Bringing Up Baby (1938) or classic divorce scenario in The Awful Truth (1937), except equipped with the foul-mouthed glory and sexual fervor inherent to reality.